Time as a measure: Elementary students positioning the hands of an analog clock

Abstract

Elementary students have difficulty with the topic of time. The present study investigated students' actions to position hour and minute hands on an analog clock to indicate particular times of the day. Using one-on-one interviews with students in Grades 2 and 4 (n = 48), we analyzed whether students were more accurate for one hand indicator (hour or minute) versus the other as well as their solution approaches as they positioned each hand. We first present a quantitative analysis of student performance to document whether hour and minute hands posed differential challenges for students as they positioned hands to indicate particular times. Results indicate the hour hand is significantly more challenging to position accurately than the minute hand. Students' solutions reflected varied approaches, including consideration of the quantitative hour-minute multiplicative relationship, attention to part-whole relations, and matching numbers from the provided time to numerals on the clock. We discuss implications for theory and instruction, including the relationship of time to length measure learning trajectories and the current treatment of time in K-12 mathematics standards for the United States.

The invisible quantity: time intervals in early algebra / La cantidad invisible: los intervalos de tiempo en el álgebra temprana

“…I present here a case study of a high-achieving grade-two student working with an analogue clock. With responses that were unusually explicit yet reflective of students across elementary grades (Earnest, 2017;Earnest, Gonzales, & Plant, 2018), this case study illuminates the potential utility of the clock as a mediational tool to support students' access to symbol systems used to capture change over time situations.…”

“…Findings indicated many students come to treat an analogue clock's structure in ways that are inconsistent with interval properties. Instead, many students draw upon numeric information and procedures (Earnest et al, 2018). For example, a typical fourth-grader interpreted a clock indicating 7:00 as 'six o'clock' (Earnest, 2017).…”

“…En el artículo se presenta un estudio de caso del trabajo realizado por una alumna avanzada de segundo curso de primaria con un reloj analógico. A través de unas respuestas atípicamente explícitas y reflexivas para un estudiante de primaria (Earnest, 2017;Earnest, Gonzales, & Plant, 2018), este estudio ilustra la utilidad potencial del reloj como herramienta de medición para facilitar el acceso de los más jóvenes a los sistemas simbólicos utilizados para reflejar el cambio en situaciones temporales. Las representaciones convencionales y sus normas no las han inventado los estudiantes, que no siempre las comprenden en un sentido matemático convencional.…”

“…Los resultados indican que muchos estudiantes gestionan la estructura de un reloj analógico de manera inconsistente con las propiedades de los intervalos. Por el contrario, muchos recurren a información y procedimientos numéricos (Earnest et al, 2018). Por ejemplo, un alumno típico de cuarto grado interpretó la hora de un reloj que marcaba 07:00 como 'las seis en punto' (Earnest, 2017).…”

Learning the Concept of Absolute Value with Hawgent Dynamic Mathematics Software

“…Therefore, we are required to strive to teach students well so that students understand the concepts of each mathematical topic in general and mathematics material well in particular. Furthermore, Learning mathematics is very difficult to understand, especially abstract material, which requires many methods to understand it (Earnest, Gonzales, & Plant, 2018).…”